cppicka | R Documentation |
This function provides estimates of coverage probability from subsets of the observation window, which are a key component of balanced estimators of covariance, centred covariance, pair-correlation and gliding box lacunarity.
cppicka(xi, obswin = NULL, setcov_boundarythresh = NULL)
xi |
An observation of a RACS of interest as a full binary map (as an |
obswin |
If |
setcov_boundarythresh |
To avoid instabilities caused by dividing by very small quantities, if the set covariance of the observation window
is smaller than |
The plug-in moment covariance estimator (plugincvc
) uses less of the observation window than the usual coverage probability estimators.
Picka (1997, 2000) created new 'balanced' estimators of centred covariance and pair-correlation
that accounted for this difference.
A key component of Picka's estimators is an estimate of the coverage probability from the subregion of the binary map that is
the intersection between W and W shifted by vector v, where W is the observation window (p.~687, Picka, 2000).
If we treat X and W as indicator functions representing the foreground and observation window respectively,
this coverage probability estimator used by Picka is
integral(X(u) W(u) W(u - v) du) / integral(W(u) W(u - v) du).
cppicka
produces these estimates for an array of vectors v using fast Fourier transforms.
An im
object. Pixel values correspond to estimates of the coverage probability
from the subregion of the observation window, W, that is the intersection of W and W shifted by vector v, where v is the pixel location.
Kassel Liam Hingee
Picka, J.D. (1997) Variance-Reducing Modifications for Estimators of Dependence in Random Sets. Ph.D.: Illinois, USA: The University of Chicago.
Picka, J.D. (2000) Variance reducing modifications for estimators of standardized moments of random sets. Advances in Applied Probability, 32, 682-700.
xi <- heather$coarse obswindow <- Frame(heather$coarse) cp <- coverageprob(xi, obswindow) cpp1 <- cppicka(xi, obswindow)
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